The matter power spectrum as derived from large scale structure (LSS) surveys
contains two important and distinct pieces of information: an overall smooth
shape and the imprint of baryon acoustic oscillations (BAO). We investigate the
separate impact of these two types of information on cosmological parameter
estimation, and show that for the simplest cosmological models, the broad-band
shape information currently contained in the SDSS DR7 halo power spectrum (HPS)
is by far superseded by geometric information derived from the baryonic
features. An immediate corollary is that contrary to popular beliefs, the upper
limit on the neutrino mass m_\nu presently derived from LSS combined with
cosmic microwave background (CMB) data does not in fact arise from the possible
small-scale power suppression due to neutrino free-streaming, if we limit the
model framework to minimal LambdaCDM+m_\nu. However, in more complicated
models, such as those extended with extra light degrees of freedom and a dark
energy equation of state parameter w differing from -1, shape information
becomes crucial for the resolution of parameter degeneracies. This conclusion
will remain true even when data from the Planck surveyor become available. In
the course of our analysis, we introduce a new dewiggling procedure that allows
us to extend consistently the use of the SDSS HPS to models with an arbitrary
sound horizon at decoupling. All the cases considered here are compatible with
the conservative 95%-bounds \sum m_\nu < 1.16 eV, N_eff = 4.8 \pm 2.0.

The authors compare how much information there in the BAO peak compared to the overall shape of the large-scale structure power spectrum. They basically conclude that at present, the information in the LSS data (when combined with the CMB) is dominated by the BAO scale.

For me, the model-independent extraction of the BAO scale via spectral analysis was particularly interesting.

There is one statement which I did not understand. On page 6 the authors explain the positive correlation between the dark energy equation of state ω and the primordial spectral index by saying that as ω becomes closer to zero (i.e. grows), the late ISW becomes larger. I would have thought that as ω goes to zero, the late ISW effect would vanish.

They're using CAMB, which if I remember correctly defaults to always using a sound speed of 1 for dark energy, regardless of what w is set to. So I don't think dark energy quite behaves like CDM as w→0, which seems to be what you're thinking of.

But I think what's more important for late ISW is that as long as w < 0, a larger w (closer to zero) means dark energy remains dominant back to higher redshift than for a more negative w, and this longer duration of dark energy dominance leads to more ISW. To put it another way: if w→ − ∞, then you get zero late ISW, because Ωde was zero up until a fraction of a second ago.

The authors compare how much information there in the BAO peak compared to the overall shape of the large-scale structure power spectrum. They basically conclude that at present, the information in the LSS data (when combined with the CMB) is dominated by the BAO scale.

I would just point out that this is a model-dependent as well as dataset-dependent statement. In the SDSS DR7 analysis, we found that using the shape information improved constraints on both mnu and Neff when combined with the CMB alone (and considering these two parameters separately). However, in this paper they're allowing both parameters to vary simultaneously (which I would guess are highly degenerate in P(k)); moreover, they've included the Riess et al. H0 constraint, which already buys you a lot in terms of breaking degeneracies with the CMB on these parameters.

In any case, it's a very interesting paper and I think they've made good improvements to how the likelihoods are implemented and clarified some confusion I had about generalizing BAO constraints to models with Neff≠3.04.

Right, I should have specified that for extended models, there is extra information in the overall shape. The authors point this out for the example of a variable number of neutrino species together with a variable dark energy equation of state. In this case, the neutrino masses, equations of state and the spectral index all benefit from the shape information.